1. Field of the Invention
This invention relates to a linear image forming apparatus which forms an image in linear form and more particularly, to a linear image forming apparatus which makes a linear image with less uneven distribution of evergy strength.
2. Description of the Prior Art
In the prior art, there was an apparatus in which a cylindrical lens was inserted in the parallel light beam, and a condenser lens was placed at the backside of the cylindrical lens to obtain a linear image pattern on the focal plane thereof for forming the final linear image. In other words, in FIGS. 1A and 1B of the accompanying drawing, the parallel light beam 11 with cylindrical cross section is dispersed only in the direction of Y by means of the cylindrical lens 12 with negative refractivity, for example, to reach the condenser lens 13. On the other hand, the constituent in the direction of X of the beam receives no dispersion at the lens 13 and thus, it is condensed on the focal plane (F) of the lens 13. However, since the constituent in the direction Y has been dispersed with the lens 12, it is not condensed on the plane (F), but on the composite focal plane F' of the cylindrical lens 12 and the condenser lens 13. As a result, the linear images 14 and 15 are formed extending in either the X or Y direction on the planes F and F'. This optical system can be said to be one with astigmatism, because the focal plane is different for the light beam of the directions X and Y. In short, the light beam is focalized on the plane F concerning the direction X, but not for the direction Y.
As known in the prior art, when the parallel light beam is condensed on a spot by means of a condenser lens, a circular distribution of light called Airy Disk is produced on the focal plane of the lens. The diametrical cross section having such a distribution of a light beam is indicated by the primary Bessel function and shown in FIG. 2A, where the abscissa represents the beam length and the ordinate the beam strength. As is also well known, the zero dimension diameter of the Airy Disk (double distance of the first strength falling to zero from the center) is given in the formula; EQU l = 1.22 (.lambda./N.A.)
Where the .tau. is the waveform of light and N.A. the aperture number of the lens. If the focal distance is represented by "f" and the diameter "D", the following equation is given: EQU N.A. = (D/2f);
It is seen that various types of light distribution are obtained, accordingly, by changing the aperture number of each light beam direction. Therefore, it is recommended to use a rectangular condenser lens with a different N.A. or an optics with an ordinary circular aperture lens fitted by a mask having a rectangular aperture for obtaining a linear image based on the above principle. In this way, the distribution of the light indicated by the formula (sin (kax)/kax.sup.2 is obtained on the focal plane of the lens used. In this formula, 2a is the aperture diameter, k = (2.pi./.tau.P) and f = the focal distance of lens. Thus, the distribution of light will be as shown in FIG. 2B, providing the image in a linear form as shown by the oblique line area. For example, if the N.A. of the direction X is 0.95 and the N.A. of the direction Y 0.10, by using a light beam with a wavelength of 4500A, the zero dimension diameter of each direction is given by the equations:
lx = (0.45/0.95) = 0.47 .mu., ly = (0.45/0.10) = 4.5 .mu.
As a result, the distribution of light is obtained in the width of 0.47 .mu. and the length of 4.5 .mu..
However, in this way, the provision of a filter is required to make one of the cross sections of the beam from a beam generator source in a rectangular shape, and thus, only the small portion of the beam generated from the source is used for the linear image formation, resulting in inefficient beam utilization.